Alternating series failing the first criteria

Asked Mar 14 '22 at 14:09

Active Mar 14 '22 at 14:09

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I am taking a Calculus course and pretty new here, but I cant find a solution to this problem anywhere.

The series is obviously alternating, so I want to check if it meets the criteria for the alternating series test. It fails the first criteria, as for small values of n it is increasing, and for large n it decreases. The divergence test gives the value of the series to be zero as n approaches infinity.

How do I go forward determening if the series diverges or converges?

asked Mar 14 '22 at 14:09

LukeDalton

Remember that the nature of a series does not depend on its first terms. – TheSilverDoe Mar 14 '22 at 14:13
It is decreasing, after a few terms (and finitely many terms don't have any impact on convergence). – lulu Mar 14 '22 at 14:13
Thanks! This was my thought, but since I still rely on my textbook and they didnt specify it, I could not be sure! – LukeDalton Mar 14 '22 at 14:17
There is also the Ratio Test. – Oscar Lanzi Mar 14 '22 at 14:27
@OscarLanzi that only works for positive series? – LukeDalton Mar 14 '22 at 16:35
@luke not at all. The Ratio Test depends only on the absolute values of the terms. – Oscar Lanzi Mar 14 '22 at 16:51

Alternating series failing the first criteria

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